HOLLYWOOD, Calif. — Lamar Odom has reportedly made good on his promise to have a baby right away with wife Khloe Kardashian.

According to RadarOnline, Kardashian is two months pregnant with the couple's first child.

"Lamar is happy and ecstatic," a source close to the family told the celebrity gossip site, adding that Kardashian has been craving "fruit and ice cream."

While the Kardashians are reportedly jumping for joy over the news, the insider said Odom is worried about the pregnancy being played out on the family's two reality shows, Keeping Up with the Kardashians and Kourtney & Khloe Take Miami.

"They're really happy, but Lamar is a little weary of exposing his baby on TV," said the source. "He already doesn't like his life being played out for everyone to see eight months of the year."

In November, the couple appeared on Chelsea Lately, where the Los Angeles Lakers star expressed his desire to start a family right away.

"You're not pregnant?" asked Handler, who attended the couple's wedding last September.

"Soon," Odom quickly replied on behalf of his spouse.

"You're planning on having a baby soon?" inquired Handler. "You want to do that right away?"

"I do," said Odom.

Looking a bit off guard, Kardashian answered: "Okay."

"Why don't you steal Kourtney's baby," quipped Handler, referring to Khloe's older sister, who gave birth to a baby boy in December.